Lesson 6
Welcome
Notes:
价格会随着克拉大小的增加而增加。 ***
Scatterplot Review
library(ggplot2)
ggplot(aes(x=carat,y=price),data = diamonds) +
xlim(0,quantile(diamonds$carat,0.99)) +
ylim(0,quantile(diamonds$price,0.99)) +
geom_point(fill = I('#F79420'),color=I('black'),shape=21)## Warning: Removed 926 rows containing missing values (geom_point).
Price and Carat Relationship
Response:
Frances Gerety
Notes:
A diamonds is
The Rise of Diamonds
Notes:
ggpairs Function
Notes:
#install these if necessary
#install.packages('GGally')
#install.packages('scales')
#install.packages('memisc')
#install.packages('lattice')
#install.packages('MASS')
#install.packages('car')
#install.packages('reshape')
#install.packages('plyr')
# load the ggplot graphics package and the others
library(ggplot2)
library(GGally)
library(scales)
library(memisc)## Loading required package: lattice## Loading required package: MASS##
## Attaching package: 'memisc'## The following object is masked from 'package:scales':
##
## percent## The following objects are masked from 'package:stats':
##
## contr.sum, contr.treatment, contrasts## The following object is masked from 'package:base':
##
## as.array# sample 10,000 diamonds from the data set
set.seed(20022012)
diamond_samp <- diamonds[sample(1:length(diamonds$price), 10000), ]
ggpairs(diamond_samp,
lower = list(continuous = wrap("points", shape = I('.'))),
upper = list(combo = wrap("box", outlier.shape = I('.'))))## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
What are some things you notice in the ggpairs output? Response:
The Demand of Diamonds
Notes:
library(gridExtra)
plot1 <- qplot(x=price,data=diamonds,binwidth = 100,fill = I('#099DD9')) +
ggtitle('Price')
plot2 <- qplot(x=price,data=diamonds,binwidth = 0.01,fill = I('#F79420')) +
scale_x_log10() +
ggtitle('Price (log10)')
grid.arrange(plot1,plot2,ncol = 2)
Connecting Demand and Price Distributions
Notes:
Scatterplot Transformation
qplot(carat,price,data=diamonds) +
scale_y_continuous(trans = log10_trans()) +
ggtitle('Price(log10)by carat')
Create a new function to transform the carat variable
cuberoot_trans = function() trans_new('cuberoot', transform = function(x) x^(1/3),
inverse = function(x) x^3)Use the cuberoot_trans function
ggplot(aes(carat, price), data = diamonds) +
geom_point() +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat')## Warning: Removed 1683 rows containing missing values (geom_point).
Overplotting Revisited
head(sort(table(diamonds$carat),decreasing = T))##
## 0.3 0.31 1.01 0.7 0.32 1
## 2604 2249 2242 1981 1840 1558head(sort(table(diamonds$price),decreasing = T))##
## 605 802 625 828 776 698
## 132 127 126 125 124 121ggplot(aes(carat, price), data = diamonds) +
geom_point(alpha = 0.5,size = 0.75,position = 'jitter') +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat')## Warning: Removed 1691 rows containing missing values (geom_point).
Other Qualitative Factors
Notes:
Price vs. Carat and Clarity
Alter the code below.
# install and load the RColorBrewer package
#install.packages('RColorBrewer')
library(RColorBrewer)
library(ggplot2)
ggplot(aes(x = carat, y = price,color = clarity), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Clarity', reverse = T,
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Clarity')## Warning: Removed 1693 rows containing missing values (geom_point).
Clarity and Price
Response:
Price vs. Carat and Cut
Alter the code below.
ggplot(aes(x = carat, y = price, color = cut), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Cut', reverse = T,
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Cut')## Warning: Removed 1696 rows containing missing values (geom_point).
Cut and Price
Response:
Price vs. Carat and Color
Alter the code below.
ggplot(aes(x = carat, y = price, color = color), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Color',
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Color')## Warning: Removed 1688 rows containing missing values (geom_point).
Color and Price
Response:
Linear Models in R
Notes:
Response:
Building the Linear Model
Notes: 为价格建立线性模型
m1 <- lm(I(log(price)) ~ I(carat^(1/3)), data = diamonds)
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)
mtable(m1, m2, m3, m4, m5)##
## Calls:
## m1: lm(formula = I(log(price)) ~ I(carat^(1/3)), data = diamonds)
## m2: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat, data = diamonds)
## m3: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut, data = diamonds)
## m4: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color,
## data = diamonds)
## m5: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color +
## clarity, data = diamonds)
##
## ============================================================================================
## m1 m2 m3 m4 m5
## --------------------------------------------------------------------------------------------
## (Intercept) 2.821*** 1.039*** 0.874*** 0.932*** 0.415***
## (0.006) (0.019) (0.019) (0.017) (0.010)
## I(carat^(1/3)) 5.558*** 8.568*** 8.703*** 8.438*** 9.144***
## (0.007) (0.032) (0.031) (0.028) (0.016)
## carat -1.137*** -1.163*** -0.992*** -1.093***
## (0.012) (0.011) (0.010) (0.006)
## cut: .L 0.224*** 0.224*** 0.120***
## (0.004) (0.004) (0.002)
## cut: .Q -0.062*** -0.062*** -0.031***
## (0.004) (0.003) (0.002)
## cut: .C 0.051*** 0.052*** 0.014***
## (0.003) (0.003) (0.002)
## cut: ^4 0.018*** 0.018*** -0.002
## (0.003) (0.002) (0.001)
## color: .L -0.373*** -0.441***
## (0.003) (0.002)
## color: .Q -0.129*** -0.093***
## (0.003) (0.002)
## color: .C 0.001 -0.013***
## (0.003) (0.002)
## color: ^4 0.029*** 0.012***
## (0.003) (0.002)
## color: ^5 -0.016*** -0.003*
## (0.003) (0.001)
## color: ^6 -0.023*** 0.001
## (0.002) (0.001)
## clarity: .L 0.907***
## (0.003)
## clarity: .Q -0.240***
## (0.003)
## clarity: .C 0.131***
## (0.003)
## clarity: ^4 -0.063***
## (0.002)
## clarity: ^5 0.026***
## (0.002)
## clarity: ^6 -0.002
## (0.002)
## clarity: ^7 0.032***
## (0.001)
## --------------------------------------------------------------------------------------------
## R-squared 0.924 0.935 0.939 0.951 0.984
## adj. R-squared 0.924 0.935 0.939 0.951 0.984
## sigma 0.280 0.259 0.250 0.224 0.129
## F 652012.063 387489.366 138654.523 87959.467 173791.084
## p 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -7962.499 -3631.319 -1837.416 4235.240 34091.272
## Deviance 4242.831 3613.360 3380.837 2699.212 892.214
## AIC 15930.999 7270.637 3690.832 -8442.481 -68140.544
## BIC 15957.685 7306.220 3761.997 -8317.942 -67953.736
## N 53940 53940 53940 53940 53940
## ============================================================================================Notice how adding cut to our model does not help explain much of the variance in the price of diamonds. This fits with out exploration earlier.
我们的数据是从2008年开始，所以不仅要考虑通货膨胀，而且钻石市场也绝对和今天不太一样。 实际上当用模型拟合此数据，并预测市场上钻石的价格时， ***
Model Problems
Video Notes:
Research: (Take some time to come up with 2-4 problems for the model) (You should 10-20 min on this)
Response:
A Bigger, Better Data Set
Notes:
#install.packages('bitops')
#install.packages('RCurl')
library('bitops')
library('RCurl')
load("BigDiamonds.rda")The code used to obtain the data is available here: https://github.com/solomonm/diamonds-data
Building a Model Using the Big Diamonds Data Set
Notes:
diamondsbig$logprice <- log(diamondsbig$price)
m1 <- lm(logprice ~ I(carat^(1/3)),
data = diamondsbig[diamondsbig$price < 10000 &
diamondsbig$cert == "GIA",])
m2 <- update(m1, ~. + carat)
m3 <- update(m2, ~. + cut)
m4 <- update(m3, ~. + color)
m5 <- update(m4, ~. + clarity)
mtable(m1,m2,m3,m4,m5)##
## Calls:
## m1: lm(formula = logprice ~ I(carat^(1/3)), data = diamondsbig[diamondsbig$price <
## 10000 & diamondsbig$cert == "GIA", ])
## m2: lm(formula = logprice ~ I(carat^(1/3)) + carat, data = diamondsbig[diamondsbig$price <
## 10000 & diamondsbig$cert == "GIA", ])
## m3: lm(formula = logprice ~ I(carat^(1/3)) + carat + cut, data = diamondsbig[diamondsbig$price <
## 10000 & diamondsbig$cert == "GIA", ])
## m4: lm(formula = logprice ~ I(carat^(1/3)) + carat + cut + color,
## data = diamondsbig[diamondsbig$price < 10000 & diamondsbig$cert ==
## "GIA", ])
## m5: lm(formula = logprice ~ I(carat^(1/3)) + carat + cut + color +
## clarity, data = diamondsbig[diamondsbig$price < 10000 & diamondsbig$cert ==
## "GIA", ])
##
## ================================================================================================
## m1 m2 m3 m4 m5
## ------------------------------------------------------------------------------------------------
## (Intercept) 2.671*** 1.333*** 0.949*** 0.529*** -0.464***
## (0.003) (0.012) (0.012) (0.010) (0.009)
## I(carat^(1/3)) 5.839*** 8.243*** 8.633*** 8.110*** 8.320***
## (0.004) (0.022) (0.021) (0.017) (0.012)
## carat -1.061*** -1.223*** -0.782*** -0.763***
## (0.009) (0.009) (0.007) (0.005)
## cut: V.Good 0.120*** 0.090*** 0.071***
## (0.002) (0.001) (0.001)
## cut: Ideal 0.211*** 0.181*** 0.131***
## (0.002) (0.001) (0.001)
## color: K/L 0.123*** 0.117***
## (0.004) (0.003)
## color: J/L 0.312*** 0.318***
## (0.003) (0.002)
## color: I/L 0.451*** 0.469***
## (0.003) (0.002)
## color: H/L 0.569*** 0.602***
## (0.003) (0.002)
## color: G/L 0.633*** 0.665***
## (0.003) (0.002)
## color: F/L 0.687*** 0.723***
## (0.003) (0.002)
## color: E/L 0.729*** 0.756***
## (0.003) (0.002)
## color: D/L 0.812*** 0.827***
## (0.003) (0.002)
## clarity: I1 0.301***
## (0.006)
## clarity: SI2 0.607***
## (0.006)
## clarity: SI1 0.727***
## (0.006)
## clarity: VS2 0.836***
## (0.006)
## clarity: VS1 0.891***
## (0.006)
## clarity: VVS2 0.935***
## (0.006)
## clarity: VVS1 0.995***
## (0.006)
## clarity: IF 1.052***
## (0.006)
## ------------------------------------------------------------------------------------------------
## R-squared 0.888 0.892 0.899 0.937 0.969
## adj. R-squared 0.888 0.892 0.899 0.937 0.969
## sigma 0.289 0.284 0.275 0.216 0.154
## F 2700903.714 1406538.330 754405.425 423311.488 521161.443
## p 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -60137.791 -53996.269 -43339.818 37830.414 154124.270
## Deviance 28298.689 27291.534 25628.285 15874.910 7992.720
## AIC 120281.582 108000.539 86691.636 -75632.827 -308204.540
## BIC 120313.783 108043.473 86756.037 -75482.557 -307968.400
## N 338946 338946 338946 338946 338946
## ================================================================================================Predictions
Example Diamond from BlueNile: Round 1.00 Very Good I VS1 $5,601
#Be sure you’ve loaded the library memisc and have m5 saved as an object in your workspace.
thisDiamond = data.frame(carat = 1.00, cut = "V.Good",
color = "I", clarity="VS1")
modelEstimate = predict(m5, newdata = thisDiamond,
interval="prediction", level = .95)
exp(modelEstimate)## fit lwr upr
## 1 5040.436 3730.34 6810.638Evaluate how well the model predicts the BlueNile diamond’s price. Think about the fitted point estimate as well as the 95% CI.
Final Thoughts
Notes:
Click KnitHTML to see all of your hard work and to have an html page of this lesson, your answers, and your notes!